I'm close to getting the heater core out of my '86 240 and the A/C lines are on the right side of it and still connected. You can see it in the attached pic.

Does anyone know if there's a way to get the heater core out without disconnecting these lines and losing my A/C's freon?

I've looked at this removal tutorial in the link but am still kinda stumped by the A/C part of it: heater core removal

 

Looks like you have to undo the evaporator in the engine bay to give you some slack and move the lines carefully away to make space "trying" not to break them. It looks like a hell of a job! Good luck!

 

There was enough play on the lines where when I removed everything around the heater core unit box I was able to swing the entire container. I thought I'd then be able to slide the evap unit out but nope... The evap unit was packed into the container so tightly that I had to take the container apart just to remove the evap unit from it. I'm swapping the heater core out so I would've had to have done that anyway but didn't expect to just to separate it from the evap unit.

Side question: On the side of the container that has the opening to remove the evap unit (you can still see it attached in the original post picture) there's a cover that when taken off had all of this black tar-like substance all over it. I'm guessing that was to create a solid seal for the evap unit? Any idea what it's called and if it's necessary for me to put more of that black stuff back on once reassembled?

 

probably some form of butyl sealant, often supplied in ropes of various thicknesses known as butyl tape.